Stats Again - Please help. So I am doing exam prep and i am stumped

[phantasia]

I am struggling with how to get the mode and median all the other ones I did it was 20 occurrences so I just wrote them out and got the middle one for the median and the most frequent for the mode.
I am also not sure how to interpret

I also don't know what to use as n now since its not given

[gilly777]

I have some statistical backgroung but I'm nowhere near an expert so everything I tell you should be taken with a grain of salt. Here is what I think :

I believe your graph for the cumulative probability density function will look like this:
(you need an account to see links)

While the probability density functiun must look like this:
(you need an account to see links)

The Median is the value for which you have 50% above and 50% under, so here it would be 8.

The risk of damage equal or more to 6 could be 60% if you look at the graph, but I think it should actually be 75% considering you suppose to also include the probabilty the damage will be equal to 6 (so add 15%)

The Mean is basically the value ponderated by their frequency so 8.7 ? (2x0.05 + 4x0.2 + 6x0.15 + 8x0.1 + 10x0.05 + 12x0.35 + 14x0.1)

The standard deviation then would be 3.8 so everything between 4.9 and 12.5 (R million) would fall within one standard deviation from the mean.

For the percentage of the population falling within I'm not really sure but I would say 65% (thats the cumulative percentage of the values between 6 and 12 wich are the closest full values of 4.9 and 12.5 in your dataset)

I really hope this helped (then again please check everything I told you, I'm not at all sure and I do not want you to fail a test because of me )

[Sephora]

@(you need an account to see links) has gotten the graphs right. The first and last points are being connected in a circle by that graph drawing program for some reason.
I did it by hand. Excuse the extra dot at 9.



There's a 60% probability the damage will be equal to or greater than R6million. You could indicate by coloring everything right of that line.

Median is what's at 50% probability, so that's R8million. The mode is the one with the most frequency, so that's R12million because 0.35 is higher than all the other probabilities. Mode is the highest point in a regular probability function (non-cumulative).

A cumulative probability distribution function adds each probability to the previous one in the table, so you eventually get 1.0 or 100% when you keep going right in the x-axis. A regular pdf is just each probability on it's own. (Cumulative pdf tells you there's a 50% probability flood damage will be R8million or less, while a regular pdf tells you there's a 10% probability your flood damage will be R8million).

I would approach getting the standard deviation the same way I did in the (you need an account to see links) - there's no need to know the sample size (n) if you do it this way. If you know the confidence level and error of margin then you can use (you need an account to see links) but it looks like that info isn't given.

The (you need an account to see links) in statistics states that when you have a normal distribution, 68% will fall within one standard deviation of the mean, 95% will fall within two standard deviations of the mean, and 99.7% will fall between three. Based on this well known rule, I would say 68% of the population for problem F.

I might not approach the problems the same way as you're taught in class, but I hope this helps.